$g(x) = x^{2}-7x-h(x)$ $h(t) = -7t+3$ $ h(g(-8)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-8)$ . Then we'll know what to plug into the outer function. $g(-8) = (-8)^{2}+(-7)(-8)-h(-8)$ To solve for the value of $g$ , we need to solve for the value of $h(-8)$ $h(-8) = (-7)(-8)+3$ $h(-8) = 59$ That means $g(-8) = (-8)^{2}+(-7)(-8)-59$ $g(-8) = 61$ Now we know that $g(-8) = 61$ . Let's solve for $h(g(-8))$ , which is $h(61)$ $h(61) = (-7)(61)+3$ $h(61) = -424$